Updated July 2026 with official ASVAB sources

ASVAB Arithmetic Reasoning Practice Test: 124 Word Problems

Use this original ASVAB Arithmetic Reasoning practice test to learn math word problems from zero. The official ASVAB description for Arithmetic Reasoning is the ability to solve arithmetic word problems, and this page turns that official scope into a full beginner practice path with 124 original questions, answer explanations, timing context, and internal links to the ASVAB and AFQT score resources.

ASVAB Study Guide ASVAB Score Guide ASVAB Score Calculator AFQT Score Calculator ASVAB Scores by Branch General Science Practice

Official Arithmetic Reasoning Scope

Official ASVAB pages describe Arithmetic Reasoning, abbreviated AR, as the ability to solve arithmetic word problems. The official subtests page places AR in the Math domain. That is a narrow and useful intent: this is not the same page as a general ASVAB study guide, a Mathematics Knowledge formula review, or an AFQT score calculator. Arithmetic Reasoning asks whether you can read a situation, choose the operation, and compute the answer accurately.

The ASVAB program does not publish a classroom-style "curriculum" for AR with chapter objectives the way a school textbook might. The latest official public scope is the subtest description, timing table, sample-question page, calculator guidance, and score guidance. This page uses only those official ASVAB materials for test facts, then builds original practice questions around the public skill description: basic arithmetic word problems. The practice buckets below are a study map, not official score-report categories.

Original practice notice: These 124 questions are written for NUM8ERS practice. They are not real ASVAB items, not leaked test questions, and not copied from official sample questions. Use them to learn problem types, estimation habits, arithmetic setup, and no-calculator fluency.

Timing and Calculator Rules

Official CAT-ASVAB information lists Arithmetic Reasoning as 15 scored questions with a 55-minute limit when no tryout questions are present. The same official CAT-ASVAB table lists possible tryout questions and a longer time limit when tryout questions are included. The official fact sheet lists the paper-and-pencil ASVAB Arithmetic Reasoning section as 30 questions in 36 minutes. Your exact test route can differ by testing program, so follow the instructions from your recruiter, school, MEPS, MET site, or official test administrator.

Version	Official AR timing context	How to practice
CAT-ASVAB	15 scored Arithmetic Reasoning questions; 55 minutes without tryout questions.	Do 15 mixed word problems in one sitting after you understand the setup methods.
CAT-ASVAB with possible tryouts	Official CAT table lists possible tryout questions and a longer time limit when they appear.	Do not judge your performance by item count alone; answer carefully and keep moving.
P&P-ASVAB	30 Arithmetic Reasoning questions in 36 minutes on the official fact sheet.	Practice 30-question sets only after you have built reliable arithmetic setup habits.

Official ASVAB FAQs explain why the ASVAB assesses the ability to do hand calculations without a calculator. That matters for your practice. Do not train with a calculator and then expect the real test to feel the same. You need clean scratch work, multiplication facts, fraction conversion, percent sense, and the ability to estimate before committing to an answer.

CAT-ASVAB behavior also affects strategy. Official ASVAB material explains that the computer adaptive test chooses items suited to your estimated ability and that answers cannot be reviewed or changed after submission. The paper-and-pencil version allows review within the current section and has different guessing guidance. This page gives practice, but your test-day instructions always come first.

How to Use This Practice Test

If you know nothing about ASVAB Arithmetic Reasoning, do not begin by racing through all 124 questions. First learn the word-problem routine: read the question, identify what is being asked, label the given numbers, choose the operation, estimate, calculate, and check that the answer has the right unit. Speed comes after setup. Many AR misses happen because the student can do arithmetic but sets up the wrong operation.

Take questions 1-20 slowly with no timer and open every explanation.
Write down the problem type for each miss: rate, percent, ratio, average, unit conversion, money, time, or multi-step.
Retake only missed questions the next day before moving forward.
When you reach questions 51-124, start estimating before calculating.
After finishing the full test, make timed sets of 15 and 30 questions.
Use official scores, not raw practice counts, with the AFQT Score Calculator or ASVAB Score Calculator.

Arithmetic Reasoning matters for AFQT because official ASVAB score guidance lists AR as one of the four subtests used to compute AFQT, along with Mathematics Knowledge, Word Knowledge, and Paragraph Comprehension. That is why AR practice belongs close to score-planning resources, but it should not replace them. This page is for practice questions and explanations. The ASVAB Score Guide explains score types, and the ASVAB Study Guide explains the whole exam process.

Beginner Word-Problem Review

Arithmetic Reasoning is reading plus arithmetic. A student who "knows the math" can still miss if the wording is not translated correctly. The first skill is to find the question sentence. Ask, "What number am I being asked to find?" Then identify the unit: dollars, miles, minutes, gallons, people, boxes, pounds, percent, or square feet. If the answer choices have units that do not match your calculation, you probably skipped a conversion.

Operation Clues Without Overtrusting Keywords

Keywords help, but they are not enough by themselves. "Total" often points to addition. "Left" often points to subtraction. "Each" can point to multiplication or division depending on the sentence. "Per" usually means a rate, such as miles per hour, dollars per pound, or gallons per minute. "Of" in a percent problem usually points to multiplication, as in 20% of 80. But a strong student does not memorize one-word rules. A strong student asks what the situation means.

For example, if 8 boxes hold 12 cans each, the total number of cans is $8 \times 12$ . If 96 cans are packed equally into 8 boxes, the number per box is $96 \div 8$ . Both problems may use the word "boxes," but the direction is different. When solving, write a short setup before doing arithmetic. Even one line such as "96 total / 8 boxes" prevents many errors.

Rates, Unit Rates, and Work Pace

A rate compares two different units. Common AR rates include miles per hour, dollars per hour, gallons per minute, pages per day, and items per box. A unit rate tells how much for one unit. If 6 notebooks cost $18, the unit price is $3 per notebook. If a truck travels 180 miles in 3 hours, the speed is 60 miles per hour. Once you have the unit rate, multiply or divide depending on what the question asks.

Work-rate questions can be solved with the same idea. If a worker packs 24 crates in 3 hours, the worker packs 8 crates per hour. In 7 hours, that worker packs 56 crates. If a machine fills 45 bottles in 5 minutes, it fills 9 bottles per minute. Keep the units attached to your numbers while solving; "9 bottles per minute" is more meaningful than just "9."

Fractions, Ratios, and Proportions

Fractions show part of a whole. If a recipe uses 3/4 cup of flour and you make two batches, multiply by 2 to get 1 1/2 cups. Ratios compare quantities. If the ratio of red to blue tags is 3:5, there are 8 total parts. If the total is 64 tags, each part is 8 tags, so red is 24 and blue is 40. Proportions are equal ratios. If 4 batteries cost $10, then 10 batteries cost $25 because each battery costs $2.50.

Use cancellation and simplification to avoid heavy arithmetic. A ratio of 18:24 simplifies to 3:4 by dividing both parts by 6. A percent such as 25% is the same as 1/4, 50% is 1/2, 75% is 3/4, 10% is one tenth, and 20% is one fifth. These conversions are useful because the ASVAB does not require a calculator for basic percent reasoning.

Percents, Discounts, Tax, and Depreciation

Percent means "per hundred." To find 15% of $80, multiply 0.15 by 80 or find 10% plus 5%. That gives $12. For a discount, subtract the discount from the original price. A $60 item with a 25% discount has a $15 discount and a sale price of $45. For sales tax, add the tax to the price. A $50 item with 8% tax costs $54 because 8% of $50 is $4.

Do not confuse percent of a number with percent increase or decrease. If a population rises from 200 to 250, the increase is 50. The percent increase is $50 \div 200 = 0.25$ , or 25%. If equipment worth $900 loses 10% of its value, it loses $90 and is worth $810. The base matters: percent change compares the change to the starting amount, not the final amount.

Averages, Totals, and Missing Values

An average is a total divided by a number of items. If five scores average 80, the total is $5 \times 80 = 400$ . If four known scores total 318, the fifth score needed for an 80 average is $400 - 318 = 82$ . This backward average pattern appears often in practice because it checks whether you understand the meaning of average, not just the formula.

When working with averages, write "total = average times count." That single sentence solves most beginner average problems. If a runner averages 6 miles per day for 7 days, the total is 42 miles. If a delivery route totals 126 miles over 3 days, the average is 42 miles per day. Watch for weighted averages, where groups have different sizes. An average of 20 workers and an average of 10 workers cannot be combined by simply averaging the two averages unless the group sizes are equal.

Time, Distance, Money, and Measurement

Time problems often require conversion. There are 60 seconds in a minute and 60 minutes in an hour. If a job takes 1 hour 20 minutes, that is 80 minutes. If a trip starts at 9:15 and lasts 2 hours 35 minutes, it ends at 11:50. Distance problems often use distance = rate times time. If a car travels 55 miles per hour for 3 hours, it travels 165 miles. If it travels 150 miles in 5 hours, the average speed is 30 miles per hour.

Money problems usually combine unit price, quantity, tax, discount, or change. Measurement problems may use feet, inches, yards, pounds, ounces, gallons, quarts, or square units. Do not mix units without converting. If a board is 6 feet long, it is 72 inches long. If tile costs $4 per square foot and a floor has 120 square feet, the cost is $480 before any extra charges.

Estimation and Answer Choice Elimination

Estimation is not guessing. It is a check on reasonableness. If a meal costs $48 and the tip is 20%, the tip should be about $10, not $1 or $40. If a car travels about 60 miles per hour for 4 hours, the distance should be about 240 miles. Estimation helps catch decimal shifts, reversed division, and forgotten conversions.

Use answer choices as information. If three choices are much larger than your estimate, revisit the setup. If two choices differ only by a unit conversion, check the unit in the question. If an answer is negative when the situation asks for a physical quantity, it is probably not reasonable. On the CAT-ASVAB, official material says you cannot go back after submitting an answer, so build the habit of checking before you click forward.

ASVAB Arithmetic Reasoning Practice Test: 124 Questions

Answer the question before opening the explanation. If you are brand new, work without a timer on the first pass. When the setup habits are reliable, use timed sets.

A supply clerk packs 8 boxes with 14 notebooks in each box. How many notebooks are packed?
1. 112
2. 96
3. 104
4. 122
Answer and explanation
Answer: A. Multiply boxes by notebooks per box: $8 \times 14 = 112$ .
A truck carries 360 pounds of equipment in 9 equal crates. How many pounds are in each crate?
1. 36
2. 40
3. 45
4. 54
Answer and explanation
Answer: B. Divide the total weight by the number of crates: $360 \div 9 = 40$ .
A class has 27 students. If 12 are absent for training, how many students are present?
1. 18
2. 21
3. 15
4. 39
Answer and explanation
Answer: C. Subtract absent students from the total: $27 - 12 = 15$ .
A warehouse receives 125 helmets on Monday and 178 helmets on Tuesday. How many helmets were received in all?
1. 253
2. 293
3. 313
4. 303
Answer and explanation
Answer: D. Add the two shipments: $125 + 178 = 303$ .
A driver travels 48 miles in 1 hour. At the same rate, how far will the driver travel in 5 hours?
1. 240 miles
2. 192 miles
3. 220 miles
4. 288 miles
Answer and explanation
Answer: A. Distance equals rate times time: $48 \times 5 = 240$ miles.
A printer makes 18 pages per minute. How many pages does it make in 7 minutes?
1. 108
2. 126
3. 116
4. 136
Answer and explanation
Answer: B. Multiply the rate by minutes: $18 \times 7 = 126$ .
If 72 bottles are divided equally among 6 coolers, how many bottles go in each cooler?
1. 9
2. 10
3. 12
4. 11
Answer and explanation
Answer: C. Divide total bottles by coolers: $72 \div 6 = 12$ .
A recruit jogs 3 miles each morning for 6 mornings. What is the total distance jogged?
1. 9 miles
2. 12 miles
3. 24 miles
4. 18 miles
Answer and explanation
Answer: D. Multiply miles per morning by mornings: $3 \times 6 = 18$ .
A cafeteria has 84 sandwiches and sells 37. How many sandwiches remain?
1. 47
2. 43
3. 51
4. 57
Answer and explanation
Answer: A. Subtract sold from total: $84 - 37 = 47$ .
A mechanic uses 5 bolts on each panel. How many bolts are needed for 19 panels?
1. 85
2. 95
3. 90
4. 105
Answer and explanation
Answer: B. Multiply bolts per panel by panels: $5 \times 19 = 95$ .
Four equal payments total $260. What is the amount of each payment?
1. $55
2. $60
3. $65
4. $70
Answer and explanation
Answer: C. Divide the total by 4 payments: $260 \div 4 = 65$ .
A team starts with 150 water bottles. After using 64 bottles, how many are left?
1. 76
2. 84
3. 94
4. 86
Answer and explanation
Answer: D. Subtract used bottles from starting bottles: $150 - 64 = 86$ .
A store sells flashlights for $12 each. What is the cost of 9 flashlights?
1. $108
2. $96
3. $112
4. $120
Answer and explanation
Answer: A. Multiply unit cost by quantity: $12 \times 9 = 108$ .
A route is 210 miles long. If a driver has already traveled 75 miles, how many miles remain?
1. 125
2. 135
3. 130
4. 145
Answer and explanation
Answer: B. Subtract completed miles from the route: $210 - 75 = 135$ .
There are 11 shelves with 16 manuals on each shelf. How many manuals are there?
1. 166
2. 186
3. 176
4. 196
Answer and explanation
Answer: C. Multiply shelves by manuals per shelf: $11 \times 16 = 176$ .
If 96 trainees are placed into groups of 8, how many groups are formed?
1. 10
2. 11
3. 14
4. 12
Answer and explanation
Answer: D. Divide trainees by group size: $96 \div 8 = 12$ .
A fuel tank holds 24 gallons. Three tanks are full and one tank has 10 gallons. How many gallons are there in all?
1. 82
2. 58
3. 72
4. 96
Answer and explanation
Answer: A. Three full tanks hold $3 \times 24 = 72$ gallons, and $72 + 10 = 82$ .
A worker labels 240 files in 6 hours. What is the average number of files labeled per hour?
1. 30
2. 40
3. 36
4. 48
Answer and explanation
Answer: B. Divide total files by hours: $240 \div 6 = 40$ .
A squad needs 144 batteries. If batteries come in packs of 12, how many packs are needed?
1. 10
2. 11
3. 12
4. 13
Answer and explanation
Answer: C. Divide batteries needed by batteries per pack: $144 \div 12 = 12$ .
A bus has 48 seats. If 35 seats are filled, how many seats are empty?
1. 11
2. 12
3. 15
4. 13
Answer and explanation
Answer: D. Empty seats equal total seats minus filled seats: $48 - 35 = 13$ .
A recipe uses 3/4 cup of rice for one serving. How many cups are needed for 4 servings?
1. 3 cups
2. 2 cups
3. 4 cups
4. 5 cups
Answer and explanation
Answer: A. Multiply $3/4$ by 4: $4 \times 3/4 = 3$ cups.
A tank is 2/5 full. If the tank holds 50 gallons, how many gallons are in it?
1. 10
2. 20
3. 15
4. 25
Answer and explanation
Answer: B. Find $2/5$ of 50: $50 \div 5 = 10$ , and $10 \times 2 = 20$ .
There are 18 red flags and 12 blue flags. What is the ratio of red flags to blue flags in simplest form?
1. 2:3
2. 3:5
3. 3:2
4. 5:3
Answer and explanation
Answer: C. The ratio $18:12$ simplifies by dividing both numbers by 6, giving $3:2$ .
If 5 pens cost $7.50, what is the cost of one pen?
1. $1.25
2. $1.75
3. $2.00
4. $1.50
Answer and explanation
Answer: D. Divide total cost by pens: $7.50 \div 5 = 1.50$ .
A map uses 1 inch to represent 20 miles. On the map, two towns are 4 inches apart. How far apart are they?
1. 80 miles
2. 40 miles
3. 60 miles
4. 100 miles
Answer and explanation
Answer: A. Multiply 20 miles per inch by 4 inches: $20 \times 4 = 80$ miles.
A class has 30 students. If 40% are wearing boots, how many students are wearing boots?
1. 10
2. 12
3. 14
4. 18
Answer and explanation
Answer: B. 40% of 30 is $0.40 \times 30 = 12$ .
A jacket costs $80 and is discounted 25%. What is the sale price?
1. $20
2. $55
3. $60
4. $65
Answer and explanation
Answer: C. 25% of $80 is $20, so the sale price is $80 - 20 = 60$ .
A tool costs $45. Sales tax is 8%. What is the total cost?
1. $49.50
2. $50.40
3. $53.00
4. $48.60
Answer and explanation
Answer: D. 8% of $45 is $3.60, and $45 + 3.60 = 48.60$ .
A number is increased from 60 to 75. What is the percent increase?
1. 25%
2. 15%
3. 20%
4. 30%
Answer and explanation
Answer: A. The increase is 15. Divide by the original 60: $15 \div 60 = 0.25 = 25%$ .
A machine loses 10% of its value from $900. What is its new value?
1. $820
2. $810
3. $890
4. $990
Answer and explanation
Answer: B. 10% of $900 is $90, and $900 - 90 = 810$ .
If 3/8 of a shipment is damaged and the shipment has 64 items, how many items are damaged?
1. 16
2. 20
3. 24
4. 32
Answer and explanation
Answer: C. $64 \div 8 = 8$ , and $8 \times 3 = 24$ .
The ratio of instructors to students is 1:12. If there are 5 instructors, how many students are there?
1. 48
2. 55
3. 72
4. 60
Answer and explanation
Answer: D. Each instructor corresponds to 12 students, so $5 \times 12 = 60$ .
A rope is 3 1/2 yards long. How many feet long is it?
1. 10.5 feet
2. 9 feet
3. 10 feet
4. 12 feet
Answer and explanation
Answer: A. One yard is 3 feet, so $3.5 \times 3 = 10.5$ feet.
A box contains 24 parts. If 1/6 of the parts are defective, how many are not defective?
1. 4
2. 20
3. 18
4. 22
Answer and explanation
Answer: B. $1/6$ of 24 is 4 defective parts, so $24 - 4 = 20$ are not defective.
What is 15% of 200?
1. 15
2. 20
3. 30
4. 35
Answer and explanation
Answer: C. $0.15 \times 200 = 30$ .
A worker finishes 2/3 of a job in 4 hours. At the same pace, how long will the whole job take?
1. 5 hours
2. 7 hours
3. 8 hours
4. 6 hours
Answer and explanation
Answer: D. If $2/3$ takes 4 hours, then $1/3$ takes 2 hours, so the full job takes 6 hours.
A price changes from $50 to $40. What is the percent decrease?
1. 20%
2. 10%
3. 25%
4. 40%
Answer and explanation
Answer: A. The decrease is $10. Divide by the original $50: $10 \div 50 = 20%$ .
In a mix, the ratio of sand to cement is 4:1. If there are 20 pounds of sand, how many pounds of cement are needed?
1. 4
2. 5
3. 8
4. 16
Answer and explanation
Answer: B. Sand is 4 parts and cement is 1 part. If 4 parts are 20 pounds, 1 part is 5 pounds.
A meal costs $36 before tip. A 20% tip is added. What is the total?
1. $39.60
2. $42.20
3. $43.20
4. $46.00
Answer and explanation
Answer: C. 20% of $36 is $7.20, and $36 + 7.20 = 43.20$ .
A runner completes 5 miles in 40 minutes. What is the average time per mile?
1. 6 minutes
2. 7 minutes
3. 9 minutes
4. 8 minutes
Answer and explanation
Answer: D. Divide total minutes by miles: $40 \div 5 = 8$ minutes per mile.
A car travels 180 miles in 3 hours. What is its average speed?
1. 60 mph
2. 45 mph
3. 50 mph
4. 55 mph
Answer and explanation
Answer: A. Average speed is distance divided by time: $180 \div 3 = 60$ mph.
A tank fills at 6 gallons per minute. How many minutes are needed to fill 54 gallons?
1. 8
2. 9
3. 10
4. 12
Answer and explanation
Answer: B. Divide gallons by gallons per minute: $54 \div 6 = 9$ .
A train leaves at 2:15 p.m. and arrives at 5:05 p.m. How long is the trip?
1. 2 hours 40 minutes
2. 3 hours 10 minutes
3. 2 hours 50 minutes
4. 3 hours 20 minutes
Answer and explanation
Answer: C. From 2:15 to 5:05 is 2 hours and 50 minutes.
A box is 4 feet long and 3 feet wide. What is its area?
1. 7 square feet
2. 10 square feet
3. 24 square feet
4. 12 square feet
Answer and explanation
Answer: D. Area of a rectangle is length times width: $4 \times 3 = 12$ .
A rectangular room is 15 feet long and 12 feet wide. Carpet costs $3 per square foot. What is the carpet cost?
1. $540
2. $360
3. $480
4. $600
Answer and explanation
Answer: A. Area is $15 \times 12 = 180$ square feet. Cost is $180 \times 3 = 540$ .
A container holds 2 quarts. How many cups does it hold?
1. 4 cups
2. 8 cups
3. 6 cups
4. 10 cups
Answer and explanation
Answer: B. One quart is 4 cups, so 2 quarts is 8 cups.
A board is 7 feet long. How many inches long is it?
1. 72 inches
2. 78 inches
3. 84 inches
4. 96 inches
Answer and explanation
Answer: C. One foot is 12 inches, so $7 \times 12 = 84$ .
A package weighs 3 pounds 8 ounces. How many ounces is that?
1. 40
2. 48
3. 52
4. 56
Answer and explanation
Answer: D. Three pounds is $3 \times 16 = 48$ ounces, and $48 + 8 = 56$ .
A worker earns $16 per hour and works 35 hours. What is the gross pay?
1. $560
2. $520
3. $540
4. $580
Answer and explanation
Answer: A. Multiply hourly rate by hours: $16 \times 35 = 560$ .
A store buys 40 radios for $18 each and sells each for $25. What is the total profit?
1. $240
2. $280
3. $260
4. $300
Answer and explanation
Answer: B. Profit per radio is $25 - 18 = 7$ , and $40 \times 7 = 280$ .
A tank has 18 gallons. It leaks 2 gallons per hour. How many gallons remain after 5 hours?
1. 6
2. 10
3. 8
4. 13
Answer and explanation
Answer: C. The tank loses $2 \times 5 = 10$ gallons, so $18 - 10 = 8$ .
A bike trip covers 72 miles at 12 miles per hour. How many hours does the trip take?
1. 4
2. 5
3. 8
4. 6
Answer and explanation
Answer: D. Time equals distance divided by rate: $72 \div 12 = 6$ hours.
A delivery starts with 96 boxes. The driver drops off 28 boxes at one stop and 35 at another. How many boxes remain?
1. 33
2. 37
3. 43
4. 63
Answer and explanation
Answer: A. Total dropped off is $28 + 35 = 63$ . Remaining boxes are $96 - 63 = 33$ .
A parking lot has 9 rows with 18 spaces in each row. If 127 spaces are filled, how many are empty?
1. 25
2. 35
3. 45
4. 55
Answer and explanation
Answer: B. Total spaces are $9 \times 18 = 162$ . Empty spaces are $162 - 127 = 35$ .
A recipe for 6 people uses 9 cups of broth. How many cups are needed for 10 people at the same rate?
1. 12
2. 14
3. 15
4. 18
Answer and explanation
Answer: C. The rate is $9 \div 6 = 1.5$ cups per person. For 10 people, $1.5 \times 10 = 15$ .
A file download is 480 megabytes. If 60 megabytes download each minute, how many minutes are needed?
1. 6
2. 7
3. 9
4. 8
Answer and explanation
Answer: D. Divide file size by download rate: $480 \div 60 = 8$ .
The average of 12, 18, and 30 is what?
1. 20
2. 18
3. 22
4. 24
Answer and explanation
Answer: A. Add and divide by 3: $(12 + 18 + 30) \div 3 = 60 \div 3 = 20$ .
Four test scores average 75. What is the total of the four scores?
1. 250
2. 300
3. 275
4. 325
Answer and explanation
Answer: B. Total equals average times number of scores: $75 \times 4 = 300$ .
A student has scores of 70, 85, and 90. What fourth score is needed for an average of 80?
1. 65
2. 70
3. 75
4. 80
Answer and explanation
Answer: C. Four scores averaging 80 total 320. Known scores total 245, so $320 - 245 = 75$ .
A group has 6 adults and 18 children. What fraction of the group are adults?
1. 1/2
2. 1/3
3. 1/6
4. 1/4
Answer and explanation
Answer: D. There are $6 + 18 = 24$ people. Adults are $6/24 = 1/4$ .
A bag has 5 red marbles, 7 blue marbles, and 8 green marbles. What is the probability of picking a blue marble?
1. 7/20
2. 5/20
3. 8/20
4. 12/20
Answer and explanation
Answer: A. There are 20 marbles total, and 7 are blue, so the probability is $7/20$ .
A code uses 3 letters followed by 2 digits. How many total characters are in the code?
1. 6
2. 5
3. 8
4. 32
Answer and explanation
Answer: B. Add the characters: $3 + 2 = 5$ . The question asks for length, not number of possible codes.
A store sold 36 shirts on Friday and 44 on Saturday. What was the average number sold per day?
1. 38
2. 42
3. 40
4. 44
Answer and explanation
Answer: C. Add and divide by 2: $(36 + 44) \div 2 = 80 \div 2 = 40$ .
A worker paints 2 rooms in 5 hours. At the same pace, how long will 6 rooms take?
1. 10 hours
2. 12 hours
3. 18 hours
4. 15 hours
Answer and explanation
Answer: D. Six rooms is 3 times as many as 2 rooms, so the time is $5 \times 3 = 15$ hours.
A tank contains a mixture with a ratio of water to cleaner of 7:1. If the mixture has 64 gallons total, how many gallons are cleaner?
1. 8
2. 6
3. 14
4. 56
Answer and explanation
Answer: A. There are 8 total ratio parts. Each part is $64 \div 8 = 8$ , and cleaner is 1 part.
A box has 30 screws. If 20% are removed, how many screws remain?
1. 6
2. 24
3. 18
4. 26
Answer and explanation
Answer: B. 20% of 30 is 6 removed, so $30 - 6 = 24$ remain.
A lunch order has 3 sandwiches at $6 each and 4 drinks at $2 each. What is the total cost?
1. $22
2. $24
3. $26
4. $28
Answer and explanation
Answer: C. Sandwiches cost $3 \times 6 = 18$ ; drinks cost $4 \times 2 = 8$ ; total is $26.
A car uses 12 gallons to travel 300 miles. How many miles per gallon does it get?
1. 20
2. 22
3. 30
4. 25
Answer and explanation
Answer: D. Divide miles by gallons: $300 \div 12 = 25$ miles per gallon.
A worker is paid $14 per hour for 40 hours and $21 per hour for 5 overtime hours. What is the total pay?
1. $665
2. $620
3. $650
4. $700
Answer and explanation
Answer: A. Regular pay is $14 \times 40 = 560$ . Overtime is $21 \times 5 = 105$ . Total is $665.
A rectangular garden has an area of 96 square feet and a width of 8 feet. What is its length?
1. 10 feet
2. 12 feet
3. 14 feet
4. 16 feet
Answer and explanation
Answer: B. Length equals area divided by width: $96 \div 8 = 12$ feet.
A phone plan costs $35 per month plus $0.10 per extra text. If the bill is $42, how many extra texts were sent?
1. 50
2. 60
3. 70
4. 80
Answer and explanation
Answer: C. Extra text cost is $42 - 35 = 7$ dollars. At $0.10 each, $7 \div 0.10 = 70$ .
A 6-pound bag of rice costs $9. What is the cost per pound?
1. $1.25
2. $1.75
3. $2.00
4. $1.50
Answer and explanation
Answer: D. Divide cost by pounds: $9 \div 6 = 1.50$ .
A clock gains 2 minutes every 5 hours. How many minutes will it gain in 20 hours?
1. 8
2. 4
3. 6
4. 10
Answer and explanation
Answer: A. Twenty hours is four 5-hour periods, so it gains $2 \times 4 = 8$ minutes.
A shipment has 75 items. If 3 out of every 5 items pass inspection, how many pass?
1. 30
2. 45
3. 40
4. 60
Answer and explanation
Answer: B. $3/5$ of 75 is $75 \div 5 \times 3 = 45$ .
A worker spends 1 hour 45 minutes on one job and 2 hours 20 minutes on another. What is the total time?
1. 3 hours 55 minutes
2. 4 hours 15 minutes
3. 4 hours 5 minutes
4. 4 hours 25 minutes
Answer and explanation
Answer: C. Add hours and minutes: 1 hour 45 minutes plus 2 hours 20 minutes is 3 hours 65 minutes, or 4 hours 5 minutes.
A vehicle travels 45 miles per hour for 2 hours, then 60 miles per hour for 1 hour. What is the total distance?
1. 120 miles
2. 135 miles
3. 165 miles
4. 150 miles
Answer and explanation
Answer: D. The first part is $45 \times 2 = 90$ miles. Add 60 miles for the third hour: total 150.
A price after a 15% discount is based on an original price of $120. What is the sale price?
1. $102
2. $90
3. $96
4. $108
Answer and explanation
Answer: A. 15% of $120 is $18, so the sale price is $120 - 18 = 102$ .
A group orders 9 pizzas cut into 8 slices each. If 58 slices are eaten, how many slices remain?
1. 12
2. 14
3. 16
4. 18
Answer and explanation
Answer: B. Total slices are $9 \times 8 = 72$ . Remaining slices are $72 - 58 = 14$ .
A machine fills 150 containers in 25 minutes. At this rate, how many containers does it fill in 1 minute?
1. 5
2. 8
3. 6
4. 10
Answer and explanation
Answer: C. Divide containers by minutes: $150 \div 25 = 6$ .
A rectangular sign has a perimeter of 30 feet. Its length is 9 feet. What is its width?
1. 4 feet
2. 5 feet
3. 7 feet
4. 6 feet
Answer and explanation
Answer: D. Perimeter is $2L + 2W$ . $30 = 18 + 2W$ , so $2W = 12$ and $W = 6$ .
A savings account has $500 and earns 4% simple interest for one year. How much interest is earned?
1. $20
2. $16
3. $18
4. $24
Answer and explanation
Answer: A. Simple interest for one year is $0.04 \times 500 = 20$ .
A recipe uses 2 cups of mix for every 3 cups of water. If 12 cups of water are used, how many cups of mix are needed?
1. 6
2. 8
3. 10
4. 18
Answer and explanation
Answer: B. The water amount is 4 times 3 cups, so the mix is $2 \times 4 = 8$ cups.
A uniform order costs $28 per shirt and $35 per jacket. What is the total cost of 6 shirts and 4 jackets?
1. $268
2. $288
3. $308
4. $328
Answer and explanation
Answer: C. Shirts cost $6 \times 28 = 168$ . Jackets cost $4 \times 35 = 140$ . Total is $308.
A 250-mile trip is completed in 5 hours. If the return trip is 50 miles longer and the same speed is used, how long is the return trip?
1. 5 hours
2. 5.5 hours
3. 6.5 hours
4. 6 hours
Answer and explanation
Answer: D. Speed is $250 \div 5 = 50$ mph. Return distance is 300 miles, so $300 \div 50 = 6$ hours.
A clerk counts 420 forms in stacks of 35. How many stacks are there?
1. 12
2. 10
3. 11
4. 14
Answer and explanation
Answer: A. Divide forms by forms per stack: $420 \div 35 = 12$ .
A battery lasts 18 hours when used 3 hours per day. How many days will it last?
1. 5
2. 6
3. 7
4. 9
Answer and explanation
Answer: B. Divide total hours by hours per day: $18 \div 3 = 6$ days.
A tent price increases from $80 to $92. What is the percent increase?
1. 12%
2. 18%
3. 15%
4. 20%
Answer and explanation
Answer: C. The increase is $12. Divide by original price: $12 \div 80 = 0.15 = 15%$ .
A store has 120 flashlights. It sells 35% of them. How many flashlights are left?
1. 42
2. 72
3. 85
4. 78
Answer and explanation
Answer: D. 35% of 120 is 42 sold. Left over is $120 - 42 = 78$ .
A board 96 inches long is cut into pieces 12 inches long. How many pieces are made?
1. 8
2. 6
3. 7
4. 9
Answer and explanation
Answer: A. Divide total length by piece length: $96 \div 12 = 8$ .
A crew needs 2 nails for each bracket. If each shelf uses 4 brackets, how many nails are needed for 15 shelves?
1. 60
2. 120
3. 90
4. 150
Answer and explanation
Answer: B. Each shelf uses $4 \times 2 = 8$ nails. For 15 shelves, $15 \times 8 = 120$ .
A driver has 3/4 of a tank of fuel. The tank holds 16 gallons. How many gallons are in the tank?
1. 10
2. 11
3. 12
4. 14
Answer and explanation
Answer: C. $3/4$ of 16 is $16 \div 4 \times 3 = 12$ .
A class of 28 students has a ratio of boys to girls of 3:4. How many girls are in the class?
1. 12
2. 14
3. 18
4. 16
Answer and explanation
Answer: D. There are 7 total parts. Each part is $28 \div 7 = 4$ . Girls are 4 parts, or 16.
A warehouse has 5 pallets with 48 boxes each and 2 pallets with 36 boxes each. How many boxes are there?
1. 312
2. 276
3. 292
4. 336
Answer and explanation
Answer: A. $5 \times 48 = 240$ and $2 \times 36 = 72$ . Total is 312 boxes.
A monthly bill is $72 after a 20% increase. What was the bill before the increase?
1. $54
2. $60
3. $58
4. $64
Answer and explanation
Answer: B. After a 20% increase, the new bill is 120% of the old bill. $72 \div 1.2 = 60$ .
A box contains 9 small packets weighing 6 ounces each and 4 large packets weighing 10 ounces each. What is the total weight?
1. 84 ounces
2. 90 ounces
3. 94 ounces
4. 104 ounces
Answer and explanation
Answer: C. Small packets weigh $9 \times 6 = 54$ ounces. Large packets weigh $4 \times 10 = 40$ . Total is 94 ounces.
A pump removes 12 gallons per minute. How long will it take to remove 180 gallons?
1. 12 minutes
2. 18 minutes
3. 20 minutes
4. 15 minutes
Answer and explanation
Answer: D. Divide total gallons by gallons per minute: $180 \div 12 = 15$ .
A vehicle averages 24 miles per gallon. How many gallons are needed for a 216-mile trip?
1. 9
2. 8
3. 10
4. 12
Answer and explanation
Answer: A. Divide miles by miles per gallon: $216 \div 24 = 9$ .
A worker needs to make 180 copies. The copier makes 30 copies per minute. After 4 minutes, how many copies remain?
1. 30
2. 60
3. 45
4. 90
Answer and explanation
Answer: B. Four minutes makes $30 \times 4 = 120$ copies. Remaining copies are $180 - 120 = 60$ .
A bag of 60 bolts contains 15 damaged bolts. What percent of the bolts are damaged?
1. 15%
2. 20%
3. 25%
4. 30%
Answer and explanation
Answer: C. $15 \div 60 = 0.25 = 25%$ .
A person buys 3 items for $18.75 total. If the items cost the same amount, what is the price of each item?
1. $5.75
2. $6.00
3. $6.50
4. $6.25
Answer and explanation
Answer: D. Divide total cost by 3: $18.75 \div 3 = 6.25$ .
A ladder is 18 feet long. It is cut into one 7-foot piece and equal 5.5-foot pieces. How many 5.5-foot pieces can be cut from the remaining length?
1. 2
2. 1
3. 3
4. 4
Answer and explanation
Answer: A. After the 7-foot piece, $18 - 7 = 11$ feet remain. $11 \div 5.5 = 2$ .
A team completes 45% of a project on Monday and 30% on Tuesday. What percent remains?
1. 15%
2. 25%
3. 20%
4. 30%
Answer and explanation
Answer: B. Completed percent is $45% + 30% = 75%$ . Remaining percent is 25%.
A box has a length of 10 inches, width of 6 inches, and height of 4 inches. What is its volume?
1. 120 cubic inches
2. 160 cubic inches
3. 240 cubic inches
4. 200 cubic inches
Answer and explanation
Answer: C. Volume is $10 \times 6 \times 4 = 240$ cubic inches.
A worker drives 30 miles to a site and returns by the same route. Fuel costs $0.20 per mile. What is the fuel cost for the round trip?
1. $6
2. $9
3. $15
4. $12
Answer and explanation
Answer: D. Round-trip distance is 60 miles. Cost is $60 \times 0.20 = 12$ .
A uniform sleeve is 32 inches long before alteration and 29.5 inches long after alteration. How many inches were removed?
1. 2.5 inches
2. 1.5 inches
3. 2 inches
4. 3 inches
Answer and explanation
Answer: A. Subtract the final length from the original length: $32 - 29.5 = 2.5$ .
A store sells 3 batteries for $4.50. At that rate, how much do 10 batteries cost?
1. $12.00
2. $15.00
3. $13.50
4. $18.00
Answer and explanation
Answer: B. One battery costs $4.50 \div 3 = 1.50$ . Ten batteries cost $15.00.
A tank is filled to 5/8 of capacity, which is 40 gallons. What is the full capacity?
1. 50 gallons
2. 56 gallons
3. 64 gallons
4. 72 gallons
Answer and explanation
Answer: C. If $5/8$ is 40, then $1/8$ is 8, so full capacity is $8 \times 8 = 64$ .
A worker spends 25% of an 8-hour shift on paperwork. How many hours are spent on paperwork?
1. 1 hour
2. 1.5 hours
3. 2.5 hours
4. 2 hours
Answer and explanation
Answer: D. 25% is one fourth, and one fourth of 8 hours is 2 hours.
A box of 48 meals is divided so that 3/4 go to one unit and the rest go to another. How many meals go to the second unit?
1. 12
2. 10
3. 16
4. 36
Answer and explanation
Answer: A. If $3/4$ go to the first unit, $1/4$ remains. $1/4$ of 48 is 12.
A delivery van travels 132 miles using 6 gallons of fuel. If fuel efficiency stays the same, how far can it travel on 10 gallons?
1. 180 miles
2. 220 miles
3. 200 miles
4. 240 miles
Answer and explanation
Answer: B. Fuel efficiency is $132 \div 6 = 22$ miles per gallon. For 10 gallons, $22 \times 10 = 220$ .
A group buys 7 tickets at $18 each and pays a $14 service fee. What is the total cost?
1. $126
2. $132
3. $140
4. $148
Answer and explanation
Answer: C. Tickets cost $7 \times 18 = 126$ . Add the $14 fee for a total of $140.
A worker can assemble 14 kits per hour. Another worker can assemble 10 kits per hour. How many kits can they assemble together in 5 hours?
1. 90
2. 100
3. 140
4. 120
Answer and explanation
Answer: D. Together they assemble $14 + 10 = 24$ kits per hour. In 5 hours, $24 \times 5 = 120$ .
A storage bin is 80% full and contains 96 parts. How many parts does it hold when full?
1. 120
2. 108
3. 112
4. 128
Answer and explanation
Answer: A. 80% is 0.8. Full capacity is $96 \div 0.8 = 120$ .
A plane flies 540 miles in 90 minutes. What is its speed in miles per hour?
1. 300 mph
2. 360 mph
3. 330 mph
4. 400 mph
Answer and explanation
Answer: B. Ninety minutes is 1.5 hours. Speed is $540 \div 1.5 = 360$ mph.
A shipment has 240 items. The first inspector checks 1/3 of them, and the second checks 1/4 of them. How many items are checked in all?
1. 120
2. 130
3. 140
4. 150
Answer and explanation
Answer: C. $1/3$ of 240 is 80, and $1/4$ is 60. Together, $80 + 60 = 140$ .
A product costs $75 after a 25% discount. What was the original price?
1. $90
2. $95
3. $125
4. $100
Answer and explanation
Answer: D. After a 25% discount, the sale price is 75% of the original. $75 \div 0.75 = 100$ .
A tank has 20 gallons. It is filled at 5 gallons per minute until it reaches 75 gallons. How long does filling take?
1. 11 minutes
2. 9 minutes
3. 10 minutes
4. 12 minutes
Answer and explanation
Answer: A. The tank needs $75 - 20 = 55$ more gallons. At 5 gallons per minute, $55 \div 5 = 11$ .
A group of 12 people splits a bill of $156 equally. How much does each person pay?
1. $11
2. $13
3. $12
4. $14
Answer and explanation
Answer: B. Divide the total bill by people: $156 \div 12 = 13$ .
A worker finishes 3/5 of a route, leaving 18 miles. What is the total route length?
1. 30 miles
2. 36 miles
3. 45 miles
4. 60 miles
Answer and explanation
Answer: C. If $3/5$ is finished, $2/5$ remains. If $2/5 = 18$ , then $1/5 = 9$ , so the total is 45.
A store pays $320 for 8 chairs and sells them for $52 each. What is the total profit?
1. $76
2. $86
3. $106
4. $96
Answer and explanation
Answer: D. Revenue is $8 \times 52 = 416$ . Profit is $416 - 320 = 96$ .
A square field has a perimeter of 84 yards. What is the length of one side?
1. 21 yards
2. 19 yards
3. 20 yards
4. 24 yards
Answer and explanation
Answer: A. A square has four equal sides, so $84 \div 4 = 21$ yards.
A worker sorts 480 envelopes in 2 hours 40 minutes. What is the average number sorted per hour?
1. 120
2. 180
3. 160
4. 200
Answer and explanation
Answer: B. Two hours 40 minutes is $2 + 2/3 = 8/3$ hours. $480 \div 8/3 = 480 \times 3/8 = 180$ .
A machine makes 1,200 parts in 8 hours. A second machine makes parts at 75% of that rate. How many parts does the second machine make in 8 hours?
1. 750
2. 800
3. 900
4. 1,000
Answer and explanation
Answer: C. 75% of 1,200 is $0.75 \times 1200 = 900$ .
A rectangle has an area of 150 square feet. If the length is 15 feet, and border material costs $2 per foot around the perimeter, what is the border cost?
1. $80
2. $90
3. $120
4. $100
Answer and explanation
Answer: D. Width is $150 \div 15 = 10$ . Perimeter is $2(15 + 10) = 50$ feet. Cost is $50 \times 2 = 100$ .

What Your Practice Result Means

This page cannot predict an official ASVAB standard score. Official ASVAB scoring uses standard-score procedures, and AFQT is computed from official AR, MK, WK, and PC standard scores. Treat this 124-question result as a diagnostic tool for practice planning. A high raw score here means your word-problem setup is improving. A low raw score tells you which arithmetic skill needs work before you spend time on timed drills.

Practice score out of 124	Meaning	Next step
106-124	Strong practice readiness	Move to timed 15-question and 30-question mixed sets.
87-105	Good foundation with a few setup gaps	Review missed problem types and retake only those items after 24 hours.
62-86	Arithmetic basics are present, but translation is inconsistent	Review rates, percent, ratios, averages, and unit conversion before timing.
Below 62	Start with no-calculator fundamentals	Use the beginner review and explanations as lessons, not as a scored exam.

What to Study Next

ASVAB Study Guide: use this for the whole exam process, registration routes, fees, result timing, retake rules, and broad study planning.
ASVAB Score Guide: use this after you see official scores and need to understand standard scores, AFQT, percentiles, and composites.
ASVAB Score Calculator: use this for full ASVAB score-report interpretation, not raw practice-test counts.
AFQT Score Calculator: use this because Arithmetic Reasoning is one of the official AFQT subtests.
ASVAB Scores by Military Branch: use this when you need public branch context after understanding your AFQT and score report.
ASVAB General Science Practice Test: use this for a separate Science/Technical-domain practice intent, not for AR math word problems.

Official Sources Used

The ASVAB structure, AR description, timing, calculator guidance, adaptive-test context, and AFQT relationship in this page were checked against official ASVAB and ASVAB CEP materials. The 124 practice questions are original NUM8ERS study questions.

Official ASVAB: Arithmetic Reasoning sample page Official ASVAB: Sample Questions Official ASVAB: Subtests Official ASVAB: CAT-ASVAB Official ASVAB Fact Sheet PDF Official ASVAB: Preparing for the ASVAB Official ASVAB: Understanding ASVAB Scores Official ASVAB FAQs

ASVAB Arithmetic Reasoning Practice Test FAQs

Are these real ASVAB Arithmetic Reasoning questions?

No. They are original practice questions written for study. They are based on the official public AR skill description, not copied from official test forms or official sample questions.

What does Arithmetic Reasoning test?

Official ASVAB materials describe Arithmetic Reasoning as the ability to solve arithmetic word problems. It is part of the Math domain.

Does Arithmetic Reasoning count toward AFQT?

Yes. Official score guidance lists Arithmetic Reasoning as one of the four subtests used to compute AFQT, along with Mathematics Knowledge, Paragraph Comprehension, and Word Knowledge.

Can I use a calculator on ASVAB Arithmetic Reasoning?

Official ASVAB FAQs explain that the ASVAB assesses hand-calculation ability without a calculator, so practice should be done without a calculator unless an official administrator gives different instructions for an accommodation.

How many AR questions are on the real ASVAB?

Official CAT-ASVAB information lists 15 scored AR questions. The official fact sheet lists 30 AR questions on the paper-and-pencil ASVAB.

What To Study After Arithmetic Reasoning Practice

This is the first Arithmetic Reasoning set. Your next page should depend on whether the mistake came from reading the situation or from the math underneath it.

Take Arithmetic Reasoning Practice Test 2 after reviewing missed setup types and you need a fresh word-problem diagnostic.
Use Mathematics Knowledge Practice when you chose the right operation but missed the fraction, percent, equation, or geometry computation.
Use Mathematics Knowledge Practice Test 2 after the first MK review if no-calculator math still feels unstable.
Use the AFQT Score Calculator to see why AR matters for AFQT planning.
Use Word Knowledge and Paragraph Comprehension if the math is improving but reading accuracy is still hurting AFQT practice.

For official score meaning, use the ASVAB Score Guide; for full exam logistics, use the ASVAB Study Guide.